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Simplifying 15x2 + 21x = -5x2 + 22 Reorder the terms: 21x + 15x2 = -5x2 + 22 Reorder the terms: 21x + 15x2 = 22 + -5x2 Solving 21x + 15x2 = 22 + -5x2 Solving for variable 'x'. Reorder the terms: -22 + 21x + 15x2 + 5x2 = 22 + -5x2 + -22 + 5x2 Combine like terms: 15x2 + 5x2 = 20x2 -22 + 21x + 20x2 = 22 + -5x2 + -22 + 5x2 Reorder the terms: -22 + 21x + 20x2 = 22 + -22 + -5x2 + 5x2 Combine like terms: 22 + -22 = 0 -22 + 21x + 20x2 = 0 + -5x2 + 5x2 -22 + 21x + 20x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -22 + 21x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.1 + 1.05x + x2 = 0.0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 1.05x + 1.1 + x2 = 0.0 + 1.1 Reorder the terms: -1.1 + 1.1 + 1.05x + x2 = 0.0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 1.05x + x2 = 0.0 + 1.1 1.05x + x2 = 0.0 + 1.1 Combine like terms: 0.0 + 1.1 = 1.1 1.05x + x2 = 1.1 The x term is 1.05x. Take half its coefficient (0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. 1.05x + 0.275625 + x2 = 1.1 + 0.275625 Reorder the terms: 0.275625 + 1.05x + x2 = 1.1 + 0.275625 Combine like terms: 1.1 + 0.275625 = 1.375625 0.275625 + 1.05x + x2 = 1.375625 Factor a perfect square on the left side: (x + 0.525)(x + 0.525) = 1.375625 Calculate the square root of the right side: 1.172870411 Break this problem into two subproblems by setting (x + 0.525) equal to 1.172870411 and -1.172870411.Subproblem 1
x + 0.525 = 1.172870411 Simplifying x + 0.525 = 1.172870411 Reorder the terms: 0.525 + x = 1.172870411 Solving 0.525 + x = 1.172870411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = 1.172870411 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 1.172870411 + -0.525 x = 1.172870411 + -0.525 Combine like terms: 1.172870411 + -0.525 = 0.647870411 x = 0.647870411 Simplifying x = 0.647870411Subproblem 2
x + 0.525 = -1.172870411 Simplifying x + 0.525 = -1.172870411 Reorder the terms: 0.525 + x = -1.172870411 Solving 0.525 + x = -1.172870411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = -1.172870411 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -1.172870411 + -0.525 x = -1.172870411 + -0.525 Combine like terms: -1.172870411 + -0.525 = -1.697870411 x = -1.697870411 Simplifying x = -1.697870411Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.647870411, -1.697870411}
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